Shock waves in a particulate suspension

A continuum theory for the distribution of incompressible particles in an incompressible fluid is employed to study the behaviour of plane shock waves in a particulate suspension. An expression is derived for the speed of displacement in terms of the jump in the volume fraction of one of the constituents across the shock. A differential equation is derived to govern the evolutionary behaviour of the shock wave propagating into a region which is in a uniform equilibrium state before the arrival of the shock wave. The implications of this equation are examined in detail.